Lie algebras in vortex dynamics and celestial mechanics - IV

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dc.creatorBolsinov, A. V.
dc.creatorBorisov, A. V.
dc.creatorMamaev, I. S.
dc.date2005-03-30
dc.date.accessioned2026-07-07T05:36:23Z
dc.date.available2026-07-07T05:36:23Z
dc.descriptionThe work of A.V. Borisov, A.E. Pavlov, Dynamics and Statics of Vortices on a Plane and a Sphere - I (Reg. & Ch. Dynamics, 1998, Vol. 3, No 1, p.28-39) introduces a naive description of dynamics of point vortices on a plane in terms of variables of distances and areas which generate Lie-Poisson structure. Using this approach a qualitative description of dynamics of point vortices on a plane and a sphere is obtained in the works Dynamics of Three Vortices on a Plane and a Sphere - II. General compact case by A.V. Borisov, V.G. Lebedev (Reg. & Ch. Dynamics, 1998, Vol. 3, No 2, p.99-114), Dynamics of three vortices on a plane and a sphere - III. Noncompact case. Problem of collaps and scattering by A.V. Borisov, V.G. Lebedev (Reg. & Ch. Dynamics, 1998, Vol. 3, No 4, p.76-90). In this paper we consider more formal constructions of the general problem of n vortices on a plane and a sphere. The developed methods of algebraization are also applied to the classical problem of the reduction in the three-body problem.
dc.description41 pages, 17 figures
dc.identifierhttps://arxiv.org/abs/nlin/0503066
dc.identifierhttp://arxiv.org/abs/nlin/0503066
dc.identifierRegular and Chaotic Dynamics, 1999 Volume 4 Number 1
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80973
dc.subjectChaotic Dynamics
dc.subjectExactly Solvable and Integrable Systems
dc.titleLie algebras in vortex dynamics and celestial mechanics - IV
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